If your FS is not journal-enabled and you remember any "unique" string in the content of the file you can use as a search seed a simple way is to:

mount the partition ro (or unmount it, if it is possible) in order to avoid
accidental overwrite of the sectors involved

grep the partition device for the string you really know the deleted file has to contain

Of course you have to adjust -B and -A grep options, in order to be able to retrieve the entire file (set the lines before and after the searching string you have to grep). Redirect grep output on a new file and adjust it to remove exceeding heading and trailing lines.